Néron–Severi group

Summary

The Néron–Severi group of a smooth projective variety is the group of divisors modulo algebraic equivalence, equivalently the Picard group modulo its identity component. The theorem of the base, due to Severi over $\C$ and Néron in general, says that it is a finitely generated abelian group. Its rank is the Picard number, and over $\C$ it is the group of integral cohomology classes of type $(1, 1)$.